Base Expansion for Nets

Every (ut, um, s)-net N in base b with u ≥ 1 is a (t, m, s)-net in base b^u [1, Lemma 2.9].

If N is linear over F_b, the resulting net is also linear over F_b, but in general not over F_b^u. Thus the resulting net is in general not digital.

See Also

• Generalization for arbitrary OOAs

• Corresponding result for sequences

• Propagation Rule 5 in [2]

References

[1]	Harald Niederreiter. Point sets and sequences with small discrepancy. Monatshefte für Mathematik, 104(4):273–337, December 1987. doi:10.1007/BF01294651 MR918037 (89c:11120)
[2]	Harald Niederreiter. Constructions of (t, m, s)-nets and (t, s)-sequences. Finite Fields and Their Applications, 11(3):578–600, August 2005. doi:10.1016/j.ffa.2005.01.001 MR2158777 (2006c:11090)

Copyright

Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.
Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “Base Expansion for Nets.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. http://mint.sbg.ac.at/desc_NBExp.html